Apparatus for the detection of angles-of-arrival of radio frequency signals

ABSTRACT

Incoming radio frequency signals from one or more remote transmitters, that may be changing or &#34;hopping&#34; in frequency, are received at two closely spaced antennas. A pair of Chirp-Z transform processors are respectively coupled to said antennas. The transform processors are operated in synchronism and produce a pair of sampled comb filter output responses, each of which comprises a multiple of frequency &#34;bins&#34; distributed over a given spectrum. The bins are read out of the Chirp-Z processors in a synchronous sequential order, and each bin is represented by a pair of signals in phase quadrature. The phase quadrature signals of corresponding bins are multiplied in a predetermined manner and the products thereof are selectively added and subtracted to provide a predetermined function (tan Φ) of the phase difference (Φ) between the signals incident on the pair of antennas. This predetermined function is coupled to a processor that calculates a trigonometric function (sin -1 ) thereof which is indicative of the angle-of-arrival of the incident wave(s).

The invention described herein may be manufactured used, and licensed byor for the Government for governmenta1 purposes without the payment tous of any royalties thereon.

TECHNICAL FIELD

The present invention relates to the detection of angles-of-arrival(AOA) of a wide spectrum of radio frequency signals by the use ofChirp-Z transform circuits utilizing high speed charge-coupled devices.

BACKGROUND OF THE INVENTION

Various techniques exist in the prior art for finding the direction(AOA) of a radio frequency source. The most well known of these isprobably what might be termed standard heterodyning techniques. Inaccordance with these techniques a heterodyne receiver is tuned for peakoutput, and may also provide a readout of the frequency in question.Direction finding can be accomplished through the use of a highlydirectional antenna. Such techniques are very time comsuming and clearlynot possible in instances where the signal source is "hopping" orchanging rapidly in frequency.

A more sophisticated prior art technique might be categorized as theBragg cell acousto-optic technique. In this technique a laser beam isreflected from the surface of a surface acoustic wave device carrying anacoustic representation of the signal of interest and the angle ofreflection, called the Bragg angle, is measured. This angle ofreflection varies as a function of frequency and, if desired, can beused for frequency determination. The angle-of-arrival at the antennaeof such a system is determined by measuring the time the incoming signalarrives at each antenna. In order to make this measurement with anysignificant degree of resolution the antennae must be separated by asubstantial distance, thereby precluding the use of an airbornemeasurement platform and otherwise limiting the effective applicationand use of this technique. In addition, several measurements of a givensignal are needed since an integration is performed over several cycleswhen this technique is used.

The U.S. Pat. No. 4,443,801 to D. R. Klose et al., issued Apr. 17, 1984,discloses apparatus which performs high resolution angle-of-arrivalmeasurements on multiple signals of different frequency. The inventiondisclosed therein is of particular utility when the signal source, orsources, is "hopping" in frequency. The Klose et al patent utilizes apair of SAW Chirp-Z transform circuits for determining the phasedifference between radio frequency signals received at two closelyspaced (1/2 to 2 wavelengths) antennae. The Klose et al patent allowsone to detect a class of frequency hopping signals that hop over anextremely broad bandwidth, but it necessitates the use of a relativelycoarse detection channel or "bin" width. The concept of the Klose et alpatent is not suitable if the receiver apparatus is required to cover alarge number of frequency bins (e.g.≧256) over a broad spectrum in whichthe spectrum samples for bins for each hop are required to be of verynarrow bandwidth.

SUMMARY OF THE INVENTION

It is a primary object of the present invention to detect and measureprecisely the angle-of-arrival (AOA) of a wide spectrum of radiofrequency signals whether the same are emanating from a single hoppingsource or from a large number of sources.

A related object of the invention is to provide angle-of-arrivalapparatus that has the ability of sampling a large number of times overa given spectum, with the spectrum samples or bin widths of each hop binbeing of very narrow bandwidth.

These and other objects are attained in accordance with the presentinvention wherein incoming radio frequency signals from one or moreremote transmitters, that may be hopping in frequency, are received attwo closely spaced antennas. Each of the received signals isrespectively coupled to one of a pair of chirp-Z transform processors.The chirp-Z processors are operated in synchronism and provide a pair ofsampled comb filter output responses, each of which comprises a multipleof spectrum samples or frequency bins distributed over a predeterminedspectrum. The bins are read out of the processors in a sequential order,and in synchronism, and each bin is represented by a pair of signals(R,I) in-phase and quadrature components. The in-phase and quadraturesignals of synchronous bins contain the requisite phase differenceinformation for angle-of-arrival determination(s). The phase quadraturesignals of corresponding bins are multiplied in a predetermined mannerand the products thereof are selectively added and subtracted to providea predetermined function (tanΦ) of the relative phase shift (Φ) betweenthe separately received signals. This predetermined function is coupledto a processor that calculates a trigonometric function (sin⁻¹) thereof,which is indicative of the angle-of-arrival of the incident wave(s).

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be more fully appreciated from the following detaileddescription when the same is considered in connection with theaccompanying drawings in which:

FIG. 1 illustrates the angle-of-arrival angle sensing concept used bythe present invention; and

FIG. 2 is a schematic block diagram of angle-of-arrival apparatus inaccordance with the present invention.

DETAILED DESCRIPTION

For purposes of illustration it is assumed herein that the incomingradio frequency signals emanate from a single source or transmitter 10,as shown in FIG. 1, and that the signal source is hopping in frequency,for example, over a frequency band from 20 to 30 megahertz. However, aswill be further explained hereinafter, the system of the inventioncould, in practice, be more elaborate than the simple arrangement shownin FIG. 1, and further it is capabIe of precisely determining the AOA'sof a large number of signal transmissions which may, or may not, befrequency hopping. The two receivers 11 and 12 of FIG. 1 are separatedonly a short distance apart, typically less than 1/2 of the shortestwavelength of the incoming RF signal(s). The angle of interest (i.e. theAOA) is the angle φ with respect to the boresight 13. The equality ofthe two angles designated φ in FIG. 1 is readily apparent from simpletrigonometry principles. With a transmitter in the indicated location,the angle φ can be found by simply detecting the phase difference (Φ) ofthe incident waves on the two receivers.

In FIG. 1, the difference in distances (d) is given by:

    d=D sin φ

where D is the distance between the receivers 11 and 12. This differencein distances (d) causes an apparent phase shift Φ between the receivedsignals, which is given by: ##EQU1## where λ is the wavelength of thesignal, or ##EQU2## where v=3×10⁸ m/sec, the velocity of light and ω isthe radian frequency.

The receivers 11 and 12 serve to detect not only the existence of aspectral line (frequency) but its phase as well. Or rather, they servein the detection of the phase difference by which the same frequency isshifted between the two receivers.

Turning now to FIG. 2, the received signals are designated IN₁, and IN₂.The received signals are initially down-converted to some intermediatefrequency and, together, they bear the phase difference which isnecessary to provide AOA indications. Each of the IN signals isdelivered to a respective Chirp-Z transform circuit or processing module21 or 22. Each of the Chirp-Z transform processors is comprised of highspeed charge-coupled devices. The Chirp-Z transform circuits are similarand are described in great detail in an article entitled "Applicationsof High Speed Charge Transfer Devices" by B. T. French (a co-inventor ofthe present invention), The Fifth International Conference on CCDs,September 1979, pages 279-279n.

For completeness of the present disclosure the Chirp-Z transformalgorithm, carried out by the Chirp-Z transform system shown in FIG. 3of the cited French article, will be briefly described. The slidingChip-Z transform is defined for a sampled input X(n) as: ##EQU3## WhereN_(o) is arbitrary and is selected as N_(o) =(N-1)/2 to yield asymmetrical CCD design. The terms in front of the summation sign yield aconstant and a frequency-dependent phase terms that drop out of thephase difference calculations, hence can be safely ignored. The term##EQU4## represents the familiar prechirp multiplication. Denoting:##EQU5## which represents the convolution of the (complex) signals##EQU6## Which completes the operational description of the transformalgorithm.

The following description is for the purpose of providing a morefunctional, and perhaps more understandable, explanation of the Chirp-Ztransformation operation. The processors 21 and 22 effectively samplethe two input signals IN₁ and IN₂ in a synchronous manner. Thissynchronous sampling is guaranteed by the use of a common sampling clock23. The clock 23 may comprise a multi-stage binary counter that countsto a given count and then recycles, and it does this in a repetitivefashion. Each of the two Chirp-Z processors 2l and 22 collects a subsetof sampled input data points and manipulates these data sample points togenerate a comb filter structure and output response. The output of eachChirp-Z processor is a sequential representation of the sampled combfilter output responses. Each comb filter output response is representedas a complex quadrature signal R₁ and I₁ or R₂ and I₂, as appropriate toprocessor 21 or 22. Thus, in effect, the output of 21 or 22 is a sampleoutput of the response of a comb filter bank to the input signal. Thebins or spectrum samples of the comb filter are read out in a sequentialorder, and in synchronism between processors 21 and 22. For each binthere is a complex signal representation in sample form; that is, eachbin has an R and I associated with it. The term bin or frequency bin isused in this art to represent a small frequency window or frequencychanne1. The complex representation of the output of each frequency bin(i.e., R and I) is a representation of the received signal in whichphase information is present. The processors 21 and 22 are read out insynchronism so that any time a given frequency bin is read out of oneprocessor the corresponding frequency bin is also read out of the otherprocessor. Thus, we are able to effectively "compare" the complex outputsignal representations of these frequency bins to eventually derive AOAinformation.

Each processor channelizes a given width, intercept window into ndetection frequency bins. The output of the processors 21 and 22 is asequential or commutative read out of each one of these bins. Thecommutation process is cyclical in that over a given period of time wego through the read out of bin 1, bin 2, bin 3, etc. and then we comeback to bin 1 after a given interval. The bins are read out at a clockrate which is typically 15 to 20 megahertz. The Chirp-Z transformprocessors 21 and 22 can be designed to cover essentially any desiredfrequency band. Also, the processors can be designed to provide adesired number of bins (e.g;≧256) and each bin can comprise a verylimited channel or bandwidth, such as 10 kilohertz or even less.

The two input sequences: ##EQU7## yield two output sequences: ##EQU8##where we are interested in the phase difference between Y₁ (k) and Y₂(k) for specified values of k, but in any case k is the same for both.

The Chirp-Z outputs R₁, I₁, or R₂, I₂ are the real and imaginary partsof the spectral lines Y₁ (k) and Y₂ (k). Using the trigonometricidentity: ##EQU9## which is what the circuitry (i.e., multipliers 24-27,adder 28 and subtractor 29) following the Chirp-Z processors calculates.Multiplier 24 multiplies R₁ and I₂, multiplier 25 multiplies I₁ and R₂,and the latter is subtracted from R₁.I₂ in subtractor 29. Multiplier 26multiplies R₁ and R₂, multiplier 27 multiplies I₁ and I₂, and the latteris added to R₁.R₂ in adder 28. To repeat, this latter circuitry simplycarries out the mathematical expression: ##EQU10##

R₁ and R₂ are the in-phase components of the spectral lines and I₁ andI₂ are the quadrature components. That is, R₁ and I₁, and R₂ and I₂, arephase quadrature components of the spectral lines Y₁ (k) and Y₂ (k). Thecomplex quadrature vector representations R and I contain the requisitephase difference information for AOA determination(s).

The output signals from adder 28 and subtractor 29 are respectivelycoupled to analog-to-digital converters 31 and 32. The A-to-D converterscan be of conventional design and serve to convert the input analogsignals (I and R) to 6-8 bit digital signals, for example. Theconverters are necessary since the AOA calculation to be explainedhereinafter is best done digitally.

The next, and last, step is the calculation of the apparent angle φ(i.e., AOA) according to the expression: ##EQU11## where

    A=2πf.sub.in. D

where f_(in) is the input frequency to the processor and D is thedistance between the receivers in meters.

The composite vector representations R and I are coupled, via the A-to-Dconverters, to the arc sine processor 33. The third input to processor33 is a (digital) frequency word (f_(in)), which basically tells theprocessor the effective frequency of the incoming signal. This lattersignal is derived from either of the chirp-Z processors 21 or 22. Moreprecisely, the digital frequency signal (f_(in)) represents the middleof a particular frequency bin at a given instant in time, whichimplicitly represents the substantially frequency of the incomingsignal. The processor 33 takes these three input digital words andcomputes the angle φ in accordance with the algorithmic expression ofequation (1), above.

The arc sine processor 33 can be implemented in several different ways.A main frame, host computer, or a dedicated microprocessor, can be usedto carry out a software algorithmic computation of the angle φ inaccordance with the equation (1), above. This is a relativelystraightforward programming task. Alternatively, and for very fast realtime operation, the computation can be carried out by means of amicroprocessor and look up table(s) whose row/column matrix(es) are theR and I vectors. The resuIt of the look-up operation is followed by arelatively simple processing function to provide the desired answer (φ).

Alternatively, if the value of A in equation (1) above is a constant,the computation of φ can be performed by one division and a tabIelookup. Further, if |I|>|R| we can use ##EQU12## With such a simpleoperation we could do away with the four multipliers and two algebraicsummers and do the computation in accordance with the expression:##EQU13## This latter calculation can be performed by two divisions andthree table lookups from two tables, interspersed with a subtraction anda multiplication (if A is not constant). All of these are fastoperations which can be done by a host computer, a dedicatedmicroprocessor, or even by dedicated hardware.

As will be appreciated by those in the art, additional base lines can beused to achieve greater precision, and adjacent base lines can, in fact,share a Chirp-Z transform circuit; i.e., a Chirp-Z processor can be usedin common between two adjacent base lines. If, as previously assumed,the first base line is of a distance D=π/2, the second base line can beequal to 3π, the fourth base line equal to 4π, or 5π, or 6π. . . 10π,and so on. The provision of additional base lines increases theprecision; i.e., the more base lines used the greater the degree ofprecision obtained. As will be further appreciated by those skilled inthe art, the actual configuration of the antenna array or directionfinding antenna array is dependent upon the final system application andcan be either a linear or a non-linear configuration depending upon theneeds of the actual system.

For purposes of illustration, it was assumed that the incoming radiofrequency signal came from a single source or transmitter which hoppedin frequency. However, the invention can also be utilized to provide theangles-of-arrival of a great many signal sources, assuming each at adifferent fixed frequency. For example, using Chirp-Z processors having256 frequency bins, the system of the invention could provideangle-of-arrival indications for 256 different signal sources at thesame time.

For further illustrative purposes, assume that the typical frequencyhopping signal hops at a rate that is no faster than once every 256clock intervals; this still represents a very rapid and realistichopping rate. Assume further that in an environment of multiple hoppingsignals that these occupy, at each instant of time, unique frequencybins during the observation interval (256 clock pulse periods). Underthese conditions multiple hopping signals look, and can be handled, nodifferently than multiple non-hopping signals. Thus, during a givenobservation interval, an AOA measurement can be made for up to 256incoming signals. And, by collecting angle measurements from multipleobservation windows, and looking for angle consistency, up to 256 uniquefrequency hopping signals can be (AOA) resolved. Alternately, of course,an appropriate mixture of fixed and hopping signals can also beresolved.

Without further belaboring the point, it should be obvious at this timethat the above described arrangement is merely illustrative of theapplication and of the principles of the present invention, and numerousmodifications thereof may be devised by those skilled in the art withoutdeparting from the spirit and scope of the invention.

What is claimed is:
 1. Apparatus for detecting the angles-of-arrival ofa wide spectrum of radio frequency signals comprising a pair of closelyspaced antennas, a pair of Chirp-Z transform means each respectivelycoupled to one of said spaced antennas, said pair of transform meansbeing operated in synchronism and providing a pair of sampled combfilter output responses each of which comprises a multiple of frequencybins distributed over said spectrum, the bins being outputted from saidpair of transform means in synchronous sequential order, each frequencybin being represented by a pair of signals in phase quadrature,arithmetric means responsive to said phase quadrature signals to form apredetermind function (tanΦ) of the phase difference(Φ) between therespective signals received at said spaced antennas, and processor meanscoupled to the output of said arthmetric means for calculating from saidpredetermined function the angles-of-arrival of signals incident on saidpair of antennas.
 2. Apparatus as defined in claim 1 wherein the phasequadrature signals of synchronous bins contain the requisite phasedifference information for angle-of-arrival determinations.
 3. Apparatusas defined in claim 2 where in said arithmetric means serves to multiplythe phase quadrature signals of corresponding sychronous bins in apredetermined manner, with the products thereof selectively added andsubtracted to provide said predetermined function (tan Φ
 4. Apparatus asdefined in claim 3 wherein the phase quadrature signals R₁ and I₁, R₂and I₂ from said pair of transform means represent the real andimaginary parts of the received spectral lines or frequencies, and saidpredetermined function is given by: ##EQU14##
 5. Apparatus as defined inclaim 4 wherein the angle-of-arrival (φ) is determined as: ##EQU15##where A=2πf_(in) D, and where f_(in) is the input frequency, and D isthe distance between the antennas in meters.